The Research On Higher-order Cross Risk Aversion Behaviors And Its Financial Decision-making

In order to learn and interpret the economic and financial phenomenons in the real word, the analysis on the economic and financial decision-making under uncertainties often investigates the effects of decision-mark’s (DM’s) risk-taking behaviors on his economic decisions. Since1960s, the general risk aversion theory has become a theory-analysis foundation to discuss DM’s issues of economic decisions under risks, and it arouses plenty of studies on cross risk changes that tally with the actual economic environment and complex risk-taking behaviors of DM with cross risk preferences. Especially, besides DM’s risk aversion, risk prudence or downside risk aversion and risk temperance, higher-order cross risk attitudes such as correlation aversion, cross prudence and cross temperance etc. and the analysis on the effects of the introduction or deterioration of background risks receives increasing attentions. They not only can reveal ’anomalies’ emerge in economic and financial market, but also help to explore DM’s many specific issues of financial investment decisions on self-protection, prevention of loss risk, effort behavior and the allocation of health resources etc.In the bivariate model of excepted utility, to analyze DM’s complex higher-order cross risk aversion behaviors, we use statistics concepts of risk increase and stochastic dominance to describe precisely higher-order cross risk changes that the DMs confront, and use the signs of the cross derivatives of bivariate utility function to reflect his higher-order cross risk aversion preferences. We build the link between DM’s higher-order cross risk aversion and higher-order cross risk changes, and reveal their preference characteristic for risks allocation on assets combination with ’good’ and ’bad’.To further clarify the essence of DM’s higher-order cross risk-taking behaviors, we define the concept that DM ’pay’ a higher-order cross risk increase for avoiding another higher-order cross risk increase, and employ the rate of substitution that reflects the tradeoff between two higher-order cross risk increases to measure his intensity of higher-order Ross cross risk aversion. We use the decision for improving monetary payoff and monetary utility premium for cross risk increase to reveal the economic implications for DM’s higher-order Ross more cross risk aversion behaviors. Moreover, we analyze the effects of non-financial unavoid background risk on DMs’ higher-order Ross cross risk aversion orders. Employing DM’s higher-order Ross measure for cross risk aversion, we give his local intensity measure coefficients of higher-order cross risk aversion and interpret its economic implications.Meanwhile, we analyze the effects of DM’s higher-order (cross) risk-taking behaviors on their specific economic decisions. Firstly, employing higher-order risk changes in utility distribution caused by DM’s self-protection behaviors, we discuss the effects of his higher order risk aversion behaviors on his self-protection decisions. We find that, the demand for self-protection for DMs who are greater degree of higher-order risk aversion indexed by higher-order risk transformation relates to the direction of risk changes in utility distribution caused by his self-protection behaviors. Secondly, in the model of bivariate utility, using the research results of higher-order cross risk aversion, we study the effects of the introduction or deterioration of background risks and correlated risks on DM’s preventive activities. We give the DM’s cross risk preference conditions to make the introduction or deterioration of background risks or a decrease in the correlation between two risks leads him to invest more in prevention. In the case of multiplicative background risks, we build the link between DM’s some prevention behaviors and the coefficients of higher-order relative risk aversion not less than their benchmark values. Once more, in the model of bivariate utility, employing the research method for the issue of precautionary savings, we explore the effects of DM’s positive correlation aversion, positively quadrant dependent aversion, lottery risk dependent aversion, good background risk aversion and the probability of its occurrence on his effort investment decisions. Our research conclusions are derived by the dependence between two risks, the signs of cross derivatives of utility function and the intensity measure of cross risk aversion. Lastly, in the framework of bivariate risk, employing the research method for the issue of precautionary savings, we analyze the effects of DM’s positive correlation aversion and positively quadrant dependent aversion on his reassures allocation of health care. Our research conclusions are derived by the dependence between two risks, the sign of third derivative of utility function and the intensity measure of partial relative prudence.